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I was wondering if the sun could be audible from earth in an air-filled space scenario. We can ignore all the other disastrous consequences! Thanks!

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Let me give a more detailed back-of-the-envelope approximation, which might actually be able to decide, given the conditions of the problem, if we would be able to hear the sound of Sun.


Assumptions:

  1. The space between Earth and Sun is filled with uniform air. This is a non-physical assumption. It basically means we are ignoring the gravitational effects of both Sun and Earth; but then one should ask what keeps Sun and Earth from exploding into the space. Anyway, the question doesn't make much sense without this assumption. So, the space is filled with air at $1_{atm}$ pressure(ask the OP how :)
  2. According to Wikipedia:

    For comparison purposes, the minimum level of a pure tone at 1000 Hz has been standardized at a sound pressure of 20 micropascals. It is approximately the quietest sound a young healthy human can detect.

    Looking at some typical minimum audibility curves, one sees that the above standard limit is actually really close to the global minimum(dB is a logarithmic scale of intensity itself, so I'm being a little bit sloppy here. But at the end of my calculations, I hope a small constant coefficient won't matter much).enter image description here

  3. Sound intensity $\propto$ (amplitude)$^2 \propto (\Delta P)^2$
  4. Some amount of spherical symmetry.

Calculations:

$$I_{\odot} 4 \pi R_{\odot}^2=I_{\oplus} 4 \pi r_{\oplus}^2 \\ \Delta P _{\odot} \approx \left( \frac{r_{\oplus}}{R_{\odot}} \right)\Delta P _{\oplus} \approx \frac{1500}{7}20_{mPc}\approx 4.3 _{Pc}$$

I believe Sun is capable of creating pressure differences much higher than this, so one expects to hear Sun's noise loud and clear. One should be able to estimate typical pressure differences by looking at solar wind data.


But How loud is sun?

In order to estimate how loud sun is, we would have to concentrate on different things that might happen on Sun. A typical aspect which might be interesting are solar flares. Let's try and estimate the sound of a solar flare on earth. According to wikipedia:

A solar flare is a sudden brightening observed over the Sun's surface or the solar limb, which is interpreted as a large energy release of up to 6 × 1025 joules of energy (about a sixth of the total energy output of the Sun each second or 160,000,000,000 megatons of TNT equivalent, over 25,000 times more energy than released from the impact of Comet Shoemaker–Levy 9 with Jupiter).

So the intensity of a solar flare sound on Earth can be approximated with $1/6$ of solar constant $\approx 227_ \frac{W}{m^2}$. I have no idea how it will actually sound, but believe me that is well above a generic human's minimum hearing capability.

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    $\begingroup$ This is so beautiful answer (not only visually) that you give me no choice but upvote it ; ) $\endgroup$ – lokers Apr 7 '14 at 15:36
  • $\begingroup$ Do you disagree with mmesser314's answer about absorption? $\endgroup$ – endolith Jan 7 '17 at 15:42
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    $\begingroup$ @endolith I do disagree with him. The reason being although we have loss in the system, we still have conservation of energy. So if the system is in a stable condition, we still expect to get sound intensities comparable to solar constant. What the absorption does is making the frequency peak of the sound get flattened and spread out through many frequencies; basically turning the coherent speech of sun into a loud shout :-) $\endgroup$ – Ali Jan 16 '17 at 4:18
  • $\begingroup$ @Ali - I updated my ancient answer in response to your old one. BTW, +1 $\endgroup$ – mmesser314 Jan 6 at 2:06
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It is years later. I just saw Ali's excellent answer, but I am still going with no. See the update below.


I am going with no.

If this was a question of sound spreading with an inverse square law, the answer would be yes.

Place a cymbal at a distance where it has the same apparent diameter as the sun. On a quiet day, it would be audible. Place 4 cymbals at twice the distance. It would be just as loud.

Repeat this idea at the distance of the sun. If the average cymbal-sized patch of the sun's surface is louder than a cymbal, you should be able to hear the sun on Earth. Given the sun's atmosphere is full of shock waves and other violent events (See this paper), it sounds likely we could hear it.


But this isn't the full story. Air absorbs sound. The absorption coefficient is small, but the distance is $10^8$ miles or $1.5 * 10^{11}$ meters in round numbers. It would take 16 years for sound to reach the Earth.

Here is a calculator for atmospheric absorption. Absorption is lowest at low temperature, low humitidy, and low frequency. Under the best conditions conditions, it is about $10^-3$ dB/m. The intensity would be reduced by $1.5 * 10^{8}$ dB. So not even if we were downwind...


This post has a helioseismology link that shows sound waves travel from one side of the sun to the other with very large amplitudes. But this isn't the same thing. These are more like earthquakes than audible sound. And the sun is a power source that keeps them going.


Update

Ali makes the points that 1) uniform air is unphysical and 2) Yes, sound is absorbed, but still energy is conserved.

I had ignored these points because

We can ignore all the other disastrous consequences!

I will now address them, but I will be pretty loose about it.


Why is the Sun so hot?

The center of the Sun has a temperature of 15.7 million degrees C. This is because the Sun produces heat from nuclear fusion. The rate of energy production is very low - a cubic meter of Sun generates heat about at the same rate as a cubic meter of compost heap.

The center of a compost heap might get hot enough to start a fire, but not millions of degrees. Heat migrates to the surface of the heap and is carried away by air.

In the Sun, it might take a million years for heat to migrate to the surface (It is a long way off.) But there is no air to carry away the heat. So heat is trapped. More and more heat is produced. The temperature of the Sun rises until the surface gets hot enough to glow. A glowing surface emits light, which carries away energy and cools the Sun. It turns out that when the surface is white hot, it emits enough light to carry away energy as fast as the interior produces it.


So what happens if there is air around the Sun?

The Sun emits energy as light. It there was air, it could also emit it as sound. But air absorbs light and sound. Within 1000 miles, it would be turned into heat.

The Sun emits hot flares. This would mix with the air and heat it.

So the net result is the heat of the Sun would be trapped in the layer of air near the sun. The air would get hotter and hotter until it glowed. This is much like the Sun, but perhaps a little bigger.

Hot air expands and gets less dense.


Sounds like a red giant

In a few billion years, the Sun will run out of hyrdogen. It will start to fuse helium, which will produce a lot of heat. The surface of the Sun will get hotter. The hotter gases will expand and become less dense. Expanding will also cool the gas.

A larger but cooler surface can radiate as much energy as a small hot surface. The surface will be only red hot. The Sun will become a red giant.

The expansion and drop in density will be enormous. The Sun will expand past Earth's orbit. The density will be so low, it might be best described as red hot vacuum. Earth will vaporize.

This is a physically realistic situation as close as we can get to air around the Sun.


So what would you hear?

Nothing, even if you were fireproof. Sound at audible frequencies does not travel in near vacuum.

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Sound, in simple words is vibration of air. So in theory yes, we should hear the Sun if there was a medium like air that could transfer the vibrations. That's just my opinion, of course I can be wrong as this is purely theoretical question and answer.

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    $\begingroup$ I suppose the question is whether the sun is loud enough that we would actually be able to detect the sound from so far away... $\endgroup$ – gj255 Apr 6 '14 at 22:44
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    $\begingroup$ Good point, I didn't think that way! :) $\endgroup$ – lokers Apr 6 '14 at 22:49
  • $\begingroup$ The sun would also have to generate a frequency that we would be able to hear. $\endgroup$ – Kyle Kanos Apr 7 '14 at 0:25

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